The Percent Change Formula, Explained Simply

Percent change is how we describe the size of a jump or a drop relative to where something started. A raw difference like "up by 20" does not mean much on its own, because 20 added to 40 is huge while 20 added to 4,000 is tiny. Turning that difference into a percentage gives you a fair, comparable number no matter the starting scale, which is exactly why it shows up in finance, science, grades, and everyday shopping.

If you are brand new to percentages in general, it helps to first skim our guide on how to calculate a percentage, then come back here for the change-over-time version.

The percent change formula

Here is the whole thing in one line. Subtract the old value from the new value, divide that difference by the old value, then multiply by 100 to convert it into a percentage.

The single most important detail is the denominator. You divide by the old value, the number you started from, because percent change always answers the question "how big was this move compared to where we began." Dividing by the new value instead is the most common error people make, and it quietly produces the wrong answer every time.

How to read the sign

The formula handles direction for you automatically through its sign:

• Positive result: the value went up. A result of plus 25 means a 25 percent increase.
• Negative result: the value went down. A result of minus 25 means a 25 percent decrease.
• Zero: nothing changed. The new and old values are equal.

Because the sign already tells you the direction, you usually report the percentage as a plain positive number and describe it with words: "a 25 percent increase" or "a 25 percent decrease." The math is identical either way.

A worked example, step by step

Suppose a jacket was priced at 80 dollars last month and is now 100 dollars. What is the percent change in price?

1. Identify the old value and the new value. Old equals 80, new equals 100.
2. Subtract: 100 minus 80 equals 20. That is the raw difference.
3. Divide by the old value: 20 divided by 80 equals 0.25.
4. Multiply by 100: 0.25 times 100 equals 25.
5. Read the sign: the result is positive, so the price rose by 25 percent.

Now reverse it. The jacket goes back from 100 dollars to 80 dollars. The difference is 80 minus 100 equals minus 20, divided by the old value of 100 equals minus 0.2, times 100 equals minus 20. So it is a 20 percent decrease. Notice that the same two prices give a 25 percent rise one way and a 20 percent fall the other way. That is not a mistake. The starting point changed, so the base you divide by changed too.

Percent change quick reference chart

Use this table to sanity check your own calculations. Every row starts from an old value of 100 so the pattern is easy to see, but the same percentages hold for any starting number.

Notice that doubling a value is a 100 percent increase, while losing half of it is a 50 percent decrease. The asymmetry trips people up, but it follows directly from always dividing by the original value.

Where you will actually use it

• Money and prices: a stock that moves from 40 to 46 is up 15 percent, and a discount works the same way in reverse. Our discount calculator uses this exact logic.
• Salary and income: a raise from 50,000 to 53,000 is a 6 percent increase.
• Science and data: population, temperature, and measurement readings are routinely compared as percent change over time.
• Grades and test scores: going from 70 to 84 on two exams is a 20 percent improvement.

Percent change is closely related to a few other formulas. If you are comparing a measured value against a known true value rather than tracking a value over time, you want percent error instead. And if you are watching something grow repeatedly at the same rate, compound interest takes percent change and applies it again and again.

Common mistakes to avoid

• Dividing by the new value. Always divide by the old, original value. Using the new value gives a different, incorrect answer.
• Mixing up which number is old. Whichever value came first in time is the old value, even if it is larger.
• Forgetting the multiply by 100. Skipping it leaves you with a decimal like 0.25 instead of 25 percent.
• Confusing percent change with percentage points. Going from 10 percent to 15 percent is a 5 percentage point rise, but a 50 percent change. They are not the same thing.
• Dropping the sign too early. Keep the negative sign until the end so you know whether it is an increase or a decrease.

Good to know

If your old value is zero, percent change is undefined, because you cannot divide by zero. There is no meaningful percentage jump "from nothing," so report the raw change instead. Also remember that percent change is not reversible: a 50 percent increase followed by a 50 percent decrease does not return you to the start, since the second percentage is taken from a larger base.

Percent change tells you the size of a move relative to where it began. Change the starting point and you change the percentage.

Calculate percent change instantly

Skip the arithmetic. Enter your old value and new value below and the calculator returns the percent change, ready to read off with the correct sign.

Once the formula clicks, percent change becomes one of the most useful tools you own for making sense of numbers that move. Master the rule "subtract, divide by the old value, multiply by 100" and you can compare almost any before and after with confidence.